If a luminous source moves with respect to the medium in which it is embedded, the kinematic shift of spectral lines depends both on the relative velocity and on the (relativistic) index of refraction of the medium. This effect is frequency-dependent, which makes it distinguishable from the cosmological redshift, the gravitational redshift and the regular Doppler shift in vacuum, which are all achromatic. The refraction-dependent shift of spectral lines is considered in more detail in the case of Ia supernovae, where the thermally generated electron-positron plasma ball, which expands with relativistic speeds, constitutes the refractive medium; it turns out that the discussed effect is relatively small at the UV and visible frequencies, but it can be significantly larger at longer wavelengths (the IR band). Other examples are given in optics and in other situations, where the refraction-dependent kinematic shift of frequency can be of significance.

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Refraction-dependent kinematic shift of spectral lines

The general law of reflection concerns situations when the light ray undergoes a shift of frequency at the reflection point. For example, it governs reflection of light rays from a moving mirror (either in a vacuum or in a transparent medium), reflection from a motionless mirror coated with a layer of Raman-active molecules in the coherent-scattering regime, or external reflection of X-rays from the surface of a condensed matter sample, with partial dissipation of energy within the skin depth. The general law of reflection is derived from the extremum principle for propagation of variable-frequency light rays. It states that the angle of reflection depends not only on the angle of incidence but also on the frequency shift in the reflection point and dispersion of the refractive index of the medium in contact with the mirror. The compatibility of the general law of reflection and the special relativistic treatment of reflection is examined in detail. Applications of the new law of reflection are discussed ...

W T Chyla

Papers

II. Geometrical optics of variable-frequency light rays in special relativistic and nonrelativistic situations: The general law of reflection